共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, by using left invariant Riemannian metrics on some three-dimensional Lie groups, we construct some complete non-Riemannian Berwald spaces of non-positive flag curvature and several families of geodesically complete locally Minkowskian spaces of zero constant flag curvature. 相似文献
2.
In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We
first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics
on homogeneous spaces and, in special case, Lie groups. We then study Randers metrics of constant positive flag curvature
and complete underlying Riemannian metric on Lie groups. Finally we give some properties of those Lie groups which admit a
left invariant non-Riemannian Randers metric of Berwald type arising from a left invariant Riemannian metric and a left invariant
vector field.
相似文献
3.
We search for invariant solutions of the conformal Killing–Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on 2-forms. We show that when the Lie group is compact equipped with a bi-invariant metric or 2-step nilpotent, the only invariant solutions occur on the 3-dimensional sphere or on a Heisenberg group. We classify the 3-dimensional Lie groups with left invariant metrics carrying invariant conformal Killing–Yano 2-forms. 相似文献
4.
Klas Modin Matthew Perlmutter Stephen Marsland Robert McLachlan 《Journal of Geometry and Physics》2011
The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler–Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given, especially in the special case of easy totally geodesic submanifolds that we introduce. The setting works both in the classical finite dimensional case, and in the category of infinite dimensional Fréchet–Lie groups, in which diffeomorphism groups are included. Using the framework we give new examples of both finite and infinite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving diffeomorphisms is totally geodesic. 相似文献
5.
We consider 4-dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce local complex-valued harmonic morphisms. 相似文献
6.
7.
Left invariant flat metrics on Lie groups are revisited in terms of left-symmetric algebras which correspond to affine structures. There is a left-symmetric algebraic approach with an explicit formula to the classification theorem given by Milnor. When the positive definiteness of the metric is replaced by nondegeneracy, there are many more examples of left invariant flat pseudo-metrics, which play important roles in several fields in geometry and mathematical physics. We give certain explicit constructions of these structures. Their classification in low dimensions and some interesting examples in higher dimensions are also given. 相似文献
8.
By building on our earlier work, we establish uncertainty principles in terms of Heisenberg inequalities and of the ambiguity functions associated with magnetic structures on certain coadjoint orbits of infinite-dimensional Lie groups. These infinite-dimensional Lie groups are semidirect products of nilpotent Lie groups and invariant function spaces thereon. The recently developed magnetic Weyl calculus is recovered in the special case of function spaces on abelian Lie groups. 相似文献
9.
We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle at level 2. We also classify such representations under a certain condition. The number of the equivalence classes of irreducible representations being finite is determined by the cohomology of the manifold. 相似文献
10.
Wang Zheng-Dong 《Letters in Mathematical Physics》1996,37(4):461-465
Infinite many invariant sectors of the regular representation of loop groups are constructed in this Letter. One of these sectors contains the cyclic component of the vacuum 0 (the constant vector) of the regular representation. This shows that the regular representation of a loop group does not admit the vacuum 0 as a cyclic vector.This work was supported in part by the National Natural Science Foundation of China. 相似文献
11.
L. Defrise-Carter 《Communications in Mathematical Physics》1975,40(3):273-282
It is shown that if ann dimensional Riemannian or pseudo-Riemannian manifold admits a proper conformal scalar, every (local) conformal group is conformally isometric, and that if it admits a proper conformal gradient every (local) conformal group is conformally homothetic. In the Riemannian case there is always a conformal scalar unless the metric is conformally Euclidean. In the case of a Lorentzian 4-manifold it is proved that the only metrics with no conformal scalars (and hence the only ones admitting a (local) conformal group not conformally isometric) are either conformal to the plane wave metric with parallel rays or conformally Minkowskian. 相似文献
12.
The aim of this Letter is twofold. On the one hand, we discuss two possible definitions of complex structures on Poisson-Lie groups and we give a complete classification of the isomorphism classes of complex Lie-Poisson structures on the group SL(2, ). On the other hand, we give an algebraic characterization of a class of solutions of the Yang-Baxter equations which contains the well-known Drinfeld solutions [1]; in particular, we prove the existence of a nontrivial Lie-Poisson structure on any simply connected real semi-simple Lie Group G. Other low dimensional examples will appear elsewhere.Chercheur qualifié au FNRS. 相似文献
13.
Cornelia Vizman 《Letters in Mathematical Physics》2008,84(2-3):245-256
We present an abstract Kelvin–Noether theorem for geodesic equations on abelian Lie group extensions with right invariant metrics and we apply it to equations of hydrodynamical type. Another Kelvin–Noether theorem for a class of central extensions of semidirect products is shown. 相似文献
14.
Loki Natarajan Enriqueta Rodríguez-Carrington Joseph A. Wolf 《Letters in Mathematical Physics》1991,23(2):99-109
A direct limit
of (finite-dimensional) Lie groups has Lie algebra
and exponential map exp
G
: gG. BothG and g carry natural topologies.G is a topological group, and g is a topological Lie algebra with a natural structure of real analytic manifold. In this Letter, we show how a special growth condition, natural in certain physical settings and satisfied by the usual direct limits of classical groups, ensures thatG carries an analytic group structure such that exp
G
is a diffeomorphism from a certain open neighborhood of 0g onto an open neighborhood of 1
G
G. In the course of the argument, one sees that the structure sheaf for this analytic group structure coincides with the direct limit
C
(G
) of the sheaves of germs of analytic functions on theG
.L.N. partially supported by a University of California Dissertation Year Fellowship.E.R.C. partially supported by N.S.F. Grant DMS 89 09432.J.A.W. partially supported by N.S.F. Grant DMS 88 05816. 相似文献
15.
We prove some theorems by Drinfeld about solutions of the triangular quantum Yang-Baxter equation and corresponding quantum groups. These theorems are to be understood in the natural setting of invariant star products on a Lie group. We also set out and prove another theorem about the invariant Hochschild cohomological meaning of the quantum Yang-Baxter equation, which underlies the others. 相似文献
16.
E. Gómez González D. Hernández Serrano J.M. Muñoz Porras F.J. Plaza Martín 《Journal of Geometry and Physics》2012
In this paper we show the existence of a group acting infinitesimally transitively on the moduli space of pointed-curves and vector bundles (with formal trivialization data) and whose Lie algebra is an algebra of differential operators. The central extension of this Lie algebra induced by the determinant bundle on the Sato Grassmannian is precisely a semidirect product of a Kac–Moody algebra and the Virasoro algebra. As an application of this geometric approach, we give a local Mumford-type formula in terms of the cocycle associated with this central extension. Finally, using the original Mumford formula we show that this local formula is an infinitesimal version of a general relation in the Picard group of the moduli of vector bundles on a family of curves (without any formal trivialization). 相似文献
17.
Hatem Hamrouni 《Letters in Mathematical Physics》2007,81(2):135-150
We describe the direct integral decomposition of a quasi regular representation of a connected and simply connected nilpotent
Lie group G, which is induced from a discrete subgroup Γ. The solution is given explicitly in terms of orbital parameters. That is, the
spectrum, multiplicity and spectral measure that constitute the decomposition are described completely in terms of natural
objects associated to the co-adjoint orbits of G. We conclude with a study of the multiplicity function in certain cases.
相似文献
18.
On each orbit W of the coadjoint representation of any nilpotent (connected, simply connected) Lie group G, we construct 1-products and associated Von Neumann algebras . G acts canonically on by automorphisms. In the unique faithful, irreducible representation of , this action is implemented by the unitary irreducible representation of G corresponding to W by the Kirillov method. This construction is uniquely determined by W and gives the classification of all unitary irreducible representations of G. 相似文献
19.
We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant L2-metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of symplectic diffeomorphisms in the Kähler case. These are special cases of totally geodesic subgroups of diffeomorphisms with Lie algebras big enough to detect the vanishing of a symmetric 2-tensor field. 相似文献
20.
S. Zakrzewski 《Letters in Mathematical Physics》1994,32(1):11-23
Poisson-Lie structures on the Lorentz group are completely classified. A method applicable to an arbitrary semisimple complex Lie group (treated as real) is developed. 相似文献